Laurențiu Panaitopol

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 10, 2004, Number 3, Pages 68—71

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## Details

### Authors and affiliations

Laurențiu Panaitopol

*University of Bucharest, Faculty of Mathematics
14 Academiei St., RO–010014 Bucharest, Romania*

### Abstract

For the integer number *n* ≥ 1 written in the basis *b* ≥ 2, we denote by *s _{b}*(

*n*),

*p*(

_{b}*n*) and

*d*(

_{b}*n*) the sum, the product and the number of its digits, respectively. There are a series of more recent or older papers concerning the relationship between these numbers. For instance, one proves in {2} that, if

*b*≥ 3, then for infinitely many numbers

*m*there exists

*n*with

*d*(

_{b}*n*) =

*m*and

*s*(

_{b}*n*) =

*m*, and this property fails also for infinitely many values of

*m*.

### Keywords

- Sums and products of digits
- Inequalities
- Means

### AMS Classification

- 11A25
- 11A51

### References

- R.E. Kennedy, C. Cooper, A generalization of a result by Narkiewicz concerning large digits of powers. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 11(2000), 36–40 (2001).
- L. Panaitopol, On the relation between the digital sum and product of a natural number (in press).

## Related papers

## Cite this paper

APAPanaitopol, L. (2004). Relationship between a natural number and its digital product. Notes on Number Theory and Discrete Mathematics, 10(3), 68-71.

ChicagoPanaitopol, Laurențiu. “Relationship between a Natural Number and Its Digital Product.” Notes on Number Theory and Discrete Mathematics 10, no. 3 (2004): 68-71.

MLAPanaitopol, Laurențiu. “Relationship between a Natural Number and Its Digital Product.” Notes on Number Theory and Discrete Mathematics 10.3 (2004): 68-71. Print.